Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class Main {
    public static void main(String args[]){
        Scanner scanner=new Scanner(System.in);
        int n,h;
        n=scanner.nextInt();
        h=scanner.nextInt();
        double area=(double)h/4;
        double share=area/n;

        double a=0.5;
        for(int i=0;i<n-1;i++) {
            double r=1;
            double l=0;

            while (true) {
                double m=l+(r-l)/2;
                if(Math.abs((m * h * m * a) / 2 - (i+1)*share) <=0.00000000001){
                    System.out.println(h*m+" ");
                    break;
                }
                else if(m * h * m * a / 2>(i+1)*share) {
                    r=m;
                }
                else {
                    l=m;
                }
            }
        }
    }
}